http://support.ea.com/app/answers/detail/a_id/5291/showhome/true
Q: Can I re-download old games I purchased?
A: Absolutely. All your previous purchases are still accessible from Origin.
Q: Can I re-download my games in general?
A: If you need to, yes. Please note that your already installed and previously purchased games are safe, sound, and work in exactly the same way as before.
Q: Is there a limit to the number of computers on which I can install my game?
A: Origin enables you to access your games from any PC, anytime, anywhere. Should you have an issue, contact Origin Help and we'll get you fixed right up!
Q: Will my game download ever expire?
A: Digital download rights remain available for at least one year after purchase. Origin typically doesn’t retire games, and we’ve only retired around 10 of the 150 games we sell, and these have generally been because of the expiration of licensing rights. If you come across an issue, simply contact Origin Help and we'll reconfigure things for you.